• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.407-417
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• 2013

In this article, we characterize t-Pr$\ddot{u}$fer modules in the class of faithful multiplication modules. As a corollary, we also characterize Krull modules. Several properties of a $t$-invertible submodule of a faithful multiplication module are given.

• Korean Journal of Mathematics
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• 제20권3호
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• pp.315-321
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• 2012

In this paper, we provide the necessary and sufficient conditions for a faithful graded module to be a graded multiplication module and for a graded submodule of a faithful gr-multiplication to be gr-essential.

• 대한수학회논문집
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• 제14권1호
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• pp.1-12
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• 1999

The faithful bi-module \ulcornerM\ulcorner with its endomorphism ring End\ulcorner(M) such that M\ulcorner is flat (in other words, End\ulcorner(M)-flat, or endo-flat)and with a commutative ring R containing an identity has been studied in this paper. The chain conditions of a faithful endo-flat module \ulcornerM relative to those of the endomorphism ring End\ulcorner(M) having the zero annihilator of each non-zero endomorphism are studied.

• 충청수학회지
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• 제6권1호
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• pp.131-137
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• 1993

Let R he a commutative ring with identity and let M be a nonzero multiplication R-module. In this note we prove that M is finitely generated if M is a faithful multiplication R-module.

• Korean Journal of Mathematics
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• 제4권2호
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• pp.101-115
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• 1996

In this paper, we will show that the minimal number of generators of any four dimensional, faithful, $\mathcal{B}$(Schur algebra of size 4)-module is two. This result can be applied to classify the isomorphism classes of the class {$\mathcal{B}{\ltimes}N^2{\mid}N$ is a faithful, $\mathcal{B}$-module with $dim_k(N)=4$}.

• 대한수학회논문집
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• 제15권3호
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• pp.453-467
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• 2000

For any S-flat module RM(which will be called endoflat) with a commutaitve ring R with identity, where S is the endomorphism ring RM, the fact that every epimorphism is an automorphism has been proved and the Jacobson Radical Rad(S) of S is described as follow; Rad(S) = { f$\in$S｜Imf=Mf is small in M} = {f$\in$S｜Imf $\leq$Rad(M)}. Additionally for any quasi-injective endo-flat module RM, the fact that every monomorphism is an automorphism has been proved and the Jacobson Radical Rad(S) for any quasi-injective endo-flat module has been studied too. Also some equivalent conditions for the semi-primitivity of any faithful endo-flat module RM with the open Jacobson Radical Rad(M) and those for the semi-simplicity of any faithful endo-flat quasi-injective module RM with the closed Socle Soc(M) have been studied.

• 대한수학회논문집
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• 제13권4호
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• pp.727-733
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• 1998

In this short paper we shall find some properties on multiplication modules and prove three theorems.

• 충청수학회지
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• 제30권1호
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• pp.53-59
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• 2017

In this article, we generalize the concepts of several classes of domains (which are related to a Dedekind domain) to a torsion-free module and it is shown that for a faithful multiplication module over an integral domain, we characterize Dedekind modules, cyclic submodule modules, and discrete valuation modules in terms of factorable modules and a sort of Euclidean algorithm.

• 대한수학회지
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• 제52권6호
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• pp.1253-1270
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• 2015

Let (R, m) be a commutative Noetherian local domain, M a non-zero finitely generated R-module of dimension n > 0 and I be an ideal of R. In this paper it is shown that if $x_1,{\ldots },x_t$ ($1{\leq}t{\leq}n$) be a sub-set of a system of parameters for M, then the R-module $H^t_{(x_1,{\ldots },x_t)}$(R) is faithful, i.e., Ann $H^t_{(x_1,{\ldots },x_t)}$(R) = 0. Also, it is shown that, if $H^i_I$ (R) = 0 for all i > dim R - dim R/I, then the R-module $H^{dimR-dimR/I}_I(R)$ is faithful. These results provide some partially affirmative answers to the Lynch's conjecture in [10]. Moreover, for an ideal I of an arbitrary Noetherian ring R, we calculate the annihilator of the top local cohomology module $H^1_I(M)$, when $H^i_I(M)=0$ for all integers i > 1. Also, for such ideals we show that the finitely generated R-algebra $D_I(R)$ is a flat R-algebra.

• 대한수학회보
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• 제45권3호
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• pp.445-456
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• 2008

Let M be a right R-module, G an ordered group and ${\sigma}$ a map from G into the group of automorphisms of R. The conditions under which the Malcev-Neumann module M* ((G)) is a PS module and a p.q.Baer module are investigated in this paper. It is shown that: (1) If $M_R$ is a reduced ${\sigma}$-compatible module, then the Malcev-Neumann module M* ((G)) over a PS-module is also a PS-module; (2) If $M_R$ is a faithful ${\sigma}$-compatible module, then the Malcev-Neumann module M* ((G)) is a p.q.Baer module if and only if the right annihilator of any G-indexed family of cyclic submodules of M in R is generated by an idempotent of R.